Murray, the world No. 1, beat Spain's Nicolas Almagro 7-6 (7-4), 7-5 while Djokovic, the defending champion in Doha, took out Czech Radek Stepanek 6-3, 6-3 in tough weather conditions on Thursday, reports Efe news agency.
"It was obviously very windy and it was blowing across the court a lot. That makes timing pretty difficult," Murray said. "It was hard for everyone today."
The 29-year-old Scotsman, who won the title here in 2008 and 2009, will play third seeded Tomas Berdych of the Czech Republic in the semi-final as he tries to advance to his first championship match of 2017.
Berdych beat France's Jo-Wilfried Tsonga, the fifth seed and 2012 Qatar Open champion, 7-5, 6-3.
Djokovic, who fell out of the top spot in the rankings in November, sounded pleased with his play after the match.
"I thought in terms of my performance, under the circumstances, I put the level up again, which is great. So everything is going in the right direction," the 29-year-old Djokovic said.
The Serbian star, who has won 12 Grand Slam titles, will play Spain's Fernando Verdasco in the semifinals.
Verdasco beat big-serving Croat Ivo Karlovic, the sixth seed, 6-2, 7-5.
"He's a very complete player," Djokovic said, referring to Verdasco. "He's got weapons from the forehand side, big serve (and he's) very strong."